Question: 4. Let f(3:) = e: cos(:c). Find a formula for f()(3:). Hint: Compute the rst few derivatives and try to nd a pattern. Then prove

$4. Let f(3:) = e\": cos(:c). Find a formula for f(\")(3:).$

4. Let f(3:) = e\": cos(:c). Find a formula for f(\")(3:). Hint: Compute the rst few derivatives and try to nd a pattern. Then prove that this pattern holds for all n 2 0 by induction. The following trigonometric identity Will be very useful: cos(m) sin(9:) = cos (a: + E) . You may use it Without proof

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